What is the Least Common Multiple of 9744 and 9753?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 9744 and 9753 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9744 and 9753, than apply into the LCM equation.

GCF(9744,9753) = 3
LCM(9744,9753) = ( 9744 × 9753) / 3
LCM(9744,9753) = 95033232 / 3
LCM(9744,9753) = 31677744

Least Common Multiple (LCM) of 9744 and 9753 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9744 and 9753. First we will calculate the prime factors of 9744 and 9753.

Prime Factorization of 9744

Prime Factorization of 9753

Now multiplying the highest exponent prime factors to calculate the LCM of 9744 and 9753.

LCM(9744,9753) = 2⁴ × 3¹ × 7¹ × 29¹ × 3251¹
LCM(9744,9753) = 31677744